A simplified math model and equivalent circuit for large, uniform, multilayered gratings of encapsulated compliant tubes irradiated by plane sound waves in water

Abstract

Detailed mathematical studies of encapsulated layers of compliant tubes indicate that the elastomeric effects can be reduced to a shear viscous damping and a shear wave stiffness loading in the layer equivalent circuit, which has been shown in earlier research to be a T network. Analysis of multiple layers yields the observation that the unsymmetric tube/ layer modes are strongly coupled to the difference of the pressure across the layer while the symmetric (compliant) modes are strongly coupled to the average of the pressure around each tube. A circuit interpretation reveals all symmetric modes in parallel with their net impedance, a shunt by the main branch which consists of the antisymmetric modes in parallel, all in a common T network. The theoretical derivations, coupling impedances, equivalent circuit, and comparison with both data and a large computer model are all presented in this paper.